The invention relates to a vibration isolation apparatus and method, and more particularly to a supportive or suspension system adapted to be coupled between two elements or structures for the reduction of transmitted mechanical excitations therebetween.
Consider a conventional single degree of freedom vibration isolation system using linear viscous damping such as is presented in FIG. 1. The forces acting on the payload of mass "M", designated by the numeral 2, which is isolated relative to a foundation 3, are the spring force which is described as being equal to the spring stiffness constant "K" times the compression of spring 4 which is the isolator relative deflection, and the dissipation force which is the linear damping coefficient "C" times the rate of compression of viscous damper 6 which is the relative velocity. These two forces must be counteracted by the isolated payload mass 2 inertial force which is the payload mass coefficient "M" multiplied by the acceleration of the payload mass itself.
In the vibration isolation field it is well known that damping in linear viscous systems controls the resonant characteristics of the entire vibration isolation system. Adding damping lowers the detrimental effect of the resonance amplification. However, as the damping is increased, resonance amplification does indeed go down but the degree of high frequency vibration isolation is lowered. In fact, if the fraction of critical damping is set to unity to eliminate the effect of resonance amplification, almost all vibration isolation is lost. Even at very high frequencies above the resonant frequency, the rate of vibration isolation only increases by six decibels per octave.
Another well-known type of vibration isolation system is one in which the resonant amplification is well controlled by viscous damping but it does so in a manner so as to preserve the vibration isolation offered at high frequencies. This type of vibration isolation system uses a linear viscous damper connected to the isolated payload so as to act as a "sky hook"; the configuration of this type of vibration isolator is presented in FIG. 2. In this figure, the linear viscous damper 6 is connected to the isolated payload 2 at one end and to a stationary location in space at the other end, known as a "sky hook" 8.
It is the stationary connection which makes the passive "sky hook" damped system impossible to construct. For in the world of vibrations all masses that are accessible to the vibration isolation system are also in motion and thus do not act as a true "sky hook". Such a system can be approximated by using active vibration isolation techniques taught in my earlier patent application of which this is a continuation in part. But my earlier invention, like other active vibration isolation systems, is limited in its effectiveness in two areas. First, such systems are generally stability limited and thus cannot be just "slipped in place", so to speak, without the necessary system stabilization circuits tailored to suit the individual application. Secondly, such systems generally require power to operate and are limited in both force and motion output by power requirement limitations imposed by an individual design.
Desirable is an active vibration isolation system having a controlled damping coefficient such that its vibration isolation characteristics can be tailored as desired. Preferably, the characteristics can be tailored to approximate a "sky hook" damper.
Understanding of the present invention would be aided by a brief mathematical analysis of the "sky hook" type vibration isolation system as presented in FIG. 2. For this system, the damping force is equal to the payload's absolute velocity times the viscous damping coefficient of the damper.
The equation of motion for the "sky hook" damped vibration isolation system is presented in EQ (1); EQU M(d.sup.2 X)=K(U-X)-C(dX) (1)
In EQ (1), "dX" and "d.sup.2 X" are the velocity and acceleration, X is the displacement of the payload, K is the spring stiffness constant, C is the damping coefficient, respectively, of the payload mass M, and "U" is the time-dependent displacement of the foundation or base relative to which the payload is isolated. (Throughout the specification, the time derivative shall be symbolized for convenience without the denominator, "dt" or "dt.sup.2 ")
One solution of this equation, for the case of steady state sinusoidal vibration, is the transmissibility vector equation for the "sky hook" damper vibration isolation system. In Laplace Transformation notation, the solution is as follows: ##EQU1## where "W.sup.2.sub.n " is equal to "K" divided by "M", "zeta" is eqaual to "C" divided by the magnitude of critical damping, and "S" is the Laplace Operator.
The damping term associated with the system's fraction of critical damping, "zeta", appears in the denominator of the equation only. This is unlike the analogous solution for the system presented in FIG. 1 wherein the "zeta" term appears in both the numerator and denominator. This seemingly minor difference between the well-known equation for the transmissibility vector for the conventional isolation system and the equation for the "sky hook" damped isolation system has, however, profound effects in the manner in which viscous damping manifests itself in the overall vibration isolation characteristics. In the "sky hook" damped system, as the degree of damping is increased and the fraction of critical damping "zeta" approaches large values above unity, the amplification due to resonance disappears and vibration isolation starts at zero frequency with a peak transmissibility of unity occurring also at zero frequency. More importantly, the increase in damping used to eliminate the system's resonance also adds vibration isolation for all frequencies below the undamped resonant frequency.
For "sky-hook" type systems the effect of additional damping for small fractions of critical damping is virtually the same as for the conventionally damped vibration isolation system in the manner in which the amount of resonant amplification is reduced. However as the fraction of critical damping is increased, exceeding a value of approximately 0.2, it is observed that not only is the amplification of vibration due to the system resonance decreased but at the same time there is no loss of vibration isolation characteristics at frequencies above resonance. This effect continues even for very large fractions of critical damping.
Desireable, therefore, would be a realizable vibration isolation system which achieves or at least approximates the advantageous vibration isolation of a "sky hook" damped system.
Therefore, it should be apparent that an object of the present invention is to provide an active vibration isolation system exhibiting improved stability and requiring less power than conventional active systems.
A further object of the present invention is to provide a realizable vibration isolation system which is characterized by a transmissibility vector equation approximating that of a "sky hook" damped system, having substantially no resonant amplification.